Energy transfer measurements are widely used to measure the distance between donors and acceptors in heterogeneous environments. In nanocrystal (NC)-molecule donor–acceptor systems, NC defects can participate in electronic energy transfer (EnT) in a defect-mediated EnT process. Here, we explore whether ensemble-level spectroscopy measurements can quantify the distance between the donor defect sites in the NC and acceptor molecules. We studied defect-mediated EnT between ZnO NCs and Alexa Fluor 555 (A555) because EnT occurs via emissive NC defect sites, such as oxygen vacancies. We synthesized a size series of ZnO NCs and characterized their radii, concentration, photoluminescence (PL) lifetime, and defect PL quantum yield using a combination of transmission electron microscopy, elemental analysis, and time-resolved PL spectroscopy. The ZnO defect PL decay kinetics were analyzed using the stochastic binding (SB) and restricted geometry (RG) models. Both models assume the Förster point dipole approximation, but the RG model considers the geometry of the NC donor in the presence of multiple acceptors. The RG model revealed that the emissive defect sites are separated, on average, 0.5 nm from the A555 acceptor molecules. That is, the emissive defect sites are predominantly located at or near the surface of large NCs. The SB model revealed the average number of A555 molecules per NC and the equilibrium binding constant but did not provide meaningful information regarding the defect–acceptor distance. We conclude that ensemble-level EnT measurements can reveal the spatial distribution of defect sites in NCs without the need for interrogating the sample with a microscope.
Fluorescence resonance energy transfer (FRET) spectroscopy can reveal nanoscale distance information in heterogeneous and dynamic systems without having to interrogate the sample with a microscope. The FRET technique is based on EnT between donor and acceptor molecules, where the photo-excited donor transfers energy non-radiatively to a nearby acceptor molecule via a dipole–dipole coupling mechanism.1–3 This method is commonly used as a “spectroscopic ruler”4–7 because small changes in donor–acceptor distance (R) cause large changes in fluorescence intensities of the donor and acceptor. The large intensity changes occur because the FRET rate scales with R−6.1–3 Steady-state and/or time-resolved photoluminescence (TRPL) spectroscopy methods can quantify R, provided that photophysical properties [e.g., spectral overlap of the donor and acceptor, donor fluorescence lifetime, and quantum yield (QY)] as well as relative orientation of the donor and acceptor molecules are known. FRET spectroscopy measurements have revealed critical dynamic distance measurements in complex systems such as membrane fusion8 and conformational changes of peptides, DNA, and RNA.9–11
Nanomaterials have emerged as stable and tunable donor and acceptor materials for EnT applications.12 In particular, semiconductor nanocrystals (NCs) are attractive donor materials because they exhibit broad absorption and tunable emission profiles via particle size and shape, high photoluminescence (PL) quantum yield, and tunable surface chemistry for acceptor molecule attachment.13–15 The tunable chemistry of NC–molecule donor–acceptor systems has enabled a wide range of potential EnT-based applications such as bio-imaging,14,16 photocatalysis,13,17,18 and photon up-conversion.19–22
Förster theory has been applied to NC–molecule donor–acceptor systems.23–30 Chowdhury et al. analyzed the PL decay dynamics of 3.0 nm CdS NCs in the presence of rhodamine 6G acceptors and concluded that the EnT efficiency was 43%.31 Sadhu et al. later developed a kinetic model based on Förster theory to model CdS NC donor quenching in the presence of multiple Nile red acceptor molecules.32 The aforementioned studies use the point-dipole approximation, placing the donor dipole at the center of the NC with acceptor molecules randomly oriented around the NC. This dipole approximation is valid when the molecule is in contact with the NC surface.33,34
However, the geometry of NC–molecule systems differs from molecular donor–acceptor systems and presents challenges for quantifying R using ensemble-level energy transfer measurements. First, the significant size mismatch between the large NC donor and small acceptor molecule enables multiple acceptors to bind to a single NC donor.32,35 It is unclear whether all surface-adsorbed acceptor molecules participate equally in the energy transfer process. In addition, it is unclear to what extent EnT occurs between neighboring molecules on the NC surface in a process called homo-FRET.36 Second, the orientation of the NC dipole relative to the molecular dipole is not well defined. While the point-dipole approximation has been shown to be valid in spherical NC–molecule systems, it is unclear whether this approximation is accurate when the dipole does not reside at the center of the NC. The point-dipole approximation fails when the donor or acceptor dipole is elongated along one axis in materials such as carbon nanotubes37 and CdSe/CdS core–shell nanoparticles.38 Third, nanomaterials are heterogeneous and possess interior and surface defect sites that can influence the EnT rate,20,39–41 but the role that defects play in the EnT process is not entirely understood.
Defect-mediated EnT offers an exciting opportunity to test whether the “spectroscopic ruler” method can measure the distance between defect sites in semiconductor NCs and acceptor molecules. Emissive defect sites in NCs have been shown to participate in EnT.42,43 Beane et al. demonstrated that a single AlexaFluor dye molecule quenched the defect emission of a single ZnO NC.44 If energy flow occurs between localized sites on the ZnO NC and the acceptor molecule, then it may be possible to measure the distance between the localized defect site and the acceptor molecule using energy transfer measurements. Several studies have focused on how the rate and efficiency of defect-mediated EnT depend on spectral overlap,45,46 attachment chemistry of the acceptor,44 and the structure and composition of ZnO,47 but little attention has been paid to measurements of R in defect-mediated EnT systems. Makhal et al. concluded that emissive defect sites most likely reside at ZnO NC surfaces,48 but no systematic studies have quantified R and considered how the presence of multiple acceptors influences the value of R.
Here, we show that ensemble-level TRPL spectroscopy can determine the relative distribution of emissive defect sites in colloidal solutions of ZnO NCs. We synthesized a size series of ZnO NCs and studied defect-mediated EnT as a function of acceptor concentration using TRPL spectroscopy. For small NCs where the Förster radius (R0) is much larger than the NC radius, PL decay analyses can reveal physically meaningful information such as the NC radius, even though the model assumes nothing about the NC size. For large NCs, where the NC radius is much larger than R0, PL decay analysis can reveal the average separation distance between emissive defects and surface-adsorbed acceptors, which can be used to infer the spatial distribution of defects in the NCs. This work shows that TRPL spectroscopy can be used as a “spectroscopic ruler” in heterogeneous NC–molecule systems.
ZnO nanocrystals (NCs) were synthesized using a base hydrolysis of zinc acetate dihydrate in ethanol following the approach of Wood et al.49 In a typical reaction, 1.0 g Zn(OAc)2 · 2H2O (Sigma Aldrich) was added to 100 ml of 200 proof ethanol (Pharmco-Aaper) in a 250-ml round bottom flask. The solution was stirred and heated to 68 °C to dissolve the zinc acetate. Then, 2 ml of a 20% methanolic solution of tetramethylammonium hydroxide (TMAOH, Sigma Aldrich) was added to the flask as quickly as possible. We define the TMAOH injection step as t = 0. Subsequently, 10 ml aliquots of the growth solution were extracted from the flask at growth times ranging from t = 2 to t = 2400 min. Each aliquot was injected into 30 ml of hexanes, causing the NCs to precipitate. The mixture was centrifuged to separate the NCs from the unreacted Zn2+ and TMAOH. This washing procedure was repeated five times with hexanes. The washed NCs were suspended in spectrophotometric grade ethanol and stored at −4 °C when not in use. All reagents were used as received and without further purification.
The optical properties of ZnO NCs were characterized by UV–Vis absorption spectroscopy (HP 8452A Diode Array Spectrophotometer) and steady-state photoluminescence spectroscopy (Edinburgh Instruments FS5). All spectra were measured at room temperature in spectrophotometric grade ethanol in 1 cm quartz cuvettes. The absolute quantum yield (QY) measurement method50,51 was used to determine the PL QY of the NC defect emission (Edinburgh Instruments FS5 spectrophotometer equipped with an integrating sphere). The NC diameters were determined using transmission electron microscopy (TEM, JEOL JEM-2100F, 200 keV). All NC diameters represent the average of at least N = 50 particles (Fig. S1).
Following the approach of Yu et al.,52 we determined the molarity of the ZnO NC samples using TEM and elemental analysis. 3 ml of washed ZnO NCs were dissolved in 5% nitric acid for inductively coupled plasma-atomic emission spectroscopy (ICP-AES) analysis. The ICP-AES analysis quantified the concentration of Zn in the sample. To calculate the concentration of NCs in each aliquot, we determined the total number of NCs that could be formed from the total number of Zn atoms in the solution. We assumed that the ZnO NCs were spheres and calculated the particle volume from the TEM data in Fig. S1. We also assumed that the ZnO lattice parameters do not change with NC size. Bulk [NC] = 70 nM was chosen because this concentration reduced NC aggregation (Fig. S2). Table S1 contains the photophysical properties for all sizes of NCs.
Energy transfer measurements
All energy transfer measurements were performed with [ZnO NC] = 70 nM. This concentration was chosen because we did not observe particle aggregation as evidenced by scattering at long wavelengths in UV–Vis spectroscopy, and all samples exhibited measurable defect PL in steady-state and time-resolved PL spectroscopy. In a typical EnT experiment, we injected microliter volumes of a stock 7 μM ethanolic Alexa Fluor 555 carboxylic acid dye (A555; Thermo Fisher) solution into 3 ml of the ZnO NC sample. The steady-state emission spectra of ZnO/dye mixtures were measured at an excitation wavelength of 330 nm, which was chosen to not overlap with the ZnO bandgap emission feature. Time-resolved photoluminescence (TRPL) measurements were performed concurrently with the steady-state measurements. The PL lifetime measurements were performed on an Edinburgh Instruments FS5 equipped with a 300 nm pulsed LED (EPLED, 500 kHz). TRPL data were acquired at the defect emission of the ZnO NCs (515 nm ± 10 nm). This wavelength range was chosen because there was no spectral overlap with the acceptor emission. TRPL data were deconvoluted from the instrument response function (IRF) using Eqs. (1) and (2) as model functions. The TRPL fits presented herein have been reconvoluted with the IRF to match the data. Figure S3 shows representative examples of the IRF deconvolution procedure.
ENERGY TRANSFER MODELLING
We analyzed the TRPL decay data for ZnO NC donors as a function of NC size and acceptor concentration using two different energy transfer models. Our goal was to determine the average donor–acceptor distance, which reflects the distance between the acceptor dyes and the defects responsible for the defect-mediated EnT process.
Stochastic binding model (SB)
Sadhu et al. developed the stochastic binding model for energy transfer between semiconductor quantum dot donors and molecular dye acceptors.32 Beane et al. applied the stochastic model to study defect-mediated EnT between ZnO NC donors and Alexa Fluor dye acceptors.44 The stochastic model assumes the following: (1) energy transfer between the NC donor and dye acceptor occurs in competition with radiative decay of the NC donor, (2) the distribution of the number of dye molecules attached to one NC follows a Poisson distribution, (3) all attached dye molecules quench the donor emission equally, (4) the intrinsic decay processes of the NCs are unaffected by the attachment of the dye molecules, (5) any acceptor molecule can participate in EnT (i.e., both adsorbed and near-surface solution-phase molecules can participate in EnT). The model also accounts for the fact that the PL decay of the ZnO NC donors does not follow single exponential kinetics. The TRPL intensity of the ZnO NC donor in the absence of dye acceptors is given by the following equation:
where I0 is the intensity of the decay curve at time t = 0 s, k0 is the radiative decay rate of photo-excited NCs in the absence of the acceptor molecule, λt is the average number of non-radiative trap states per NC which are distributed according to Poisson statistics, and kqt is the quenching rate due to the presence of the non-radiative traps. The non-radiative trap term is necessary to describe the non-single exponential defect PL decay of the ZnO NCs. These traps do not participate in the EnT process.32
The TRPL decay curves of the NC donors in the presence of the acceptor are given by the following equation:
where λs is the mean number of dye molecules per NC according to Poisson statistics32,53,54 and kq is the rate of energy transfer to a single dye molecule. Hence, when a NC with n dye molecules is excited, the rate of the excited-state decay for that NC is given by k0 + nkq, and the total energy transfer rate is nkq.32
where n and n′ are the integer number of attached dye molecules per NC and the integer number of non-radiative traps, respectively. We deconvoluted the IRF from the sample response to fit all TRPL data.
The EnT efficiency is related to the number of attached dye molecules per NC and the donor–acceptor distance, R, according to the following equation:35,53
where R0 is the Forster radius or the distance at which the EnT efficiency between a single donor–acceptor pair is equal to 50%.53,55,56 We calculate R0 according to the following equation:
where κ is the orientation factor that accounts for the relative orientation of the donor and acceptor dipoles. QD is the emission quantum yield of the donor in the absence of the acceptor. J is the overlap integral of the donor emission and acceptor absorbance, and NA is Avogadro’s constant. We fit the TRPL-derived ΦEnT values using Eq. (4) to determine the ensemble-average R for each NC diameter and as a function of acceptor concentration.
Restricted geometry model (RG)
Sitt et al. developed a restricted geometry model to analyze energy transfer from zero-dimensional (0D) NC and one-dimensional (1D) nanorod donors to molecular acceptors.57 For 0D NCs, the model restricts the acceptor molecule locations to a spherical shell at the NC surface, as shown in Scheme 1. r1 and r2 are the minimum and maximum distances in nanometers from the donor to the acceptor molecules, corresponding to the inner and outer radii of the spherical shell, respectively. The restricted geometry (RG) model assumes that molecules within the shell contribute to EnT. The donor dipole is assumed to be a point dipole at the center of the spherical NC. This geometry may not be the case for the emissive defect sites in these ZnO NCs where the donor dipole of the defect may not be at the center of the NC. A complete treatment beyond the Förster point dipole approximation could be employed37,38,58–60 but is not included in the restricted geometries model.
In this work, we quantified the minimum donor–acceptor distance, r1, using the following equation:
where Cs is the concentration of acceptor molecules within the spherical shell (in units of molecules per cubic nanometer), χ is defined as , where τD is the radiative lifetime of the donor in the absence of acceptor molecules in units of nanoseconds (τD−1 = k0 in Table S1), S is the multipolar exponent (S = 6 for dipole–dipole interactions), and is the incomplete gamma function. Φret(t) curves are obtained by dividing the TRPL decay of the NC-acceptor mixtures by the TRPL decay of the NCs in the absence of the acceptors. To reduce the number of fitting parameters in Eq. (6), we assumed that , corresponding to the length of the A555 molecule. Hence, we fit Φret(t) curves with Eq. (6) to determine Cs and r1. The full derivation of Eq. (6) can be found in Ref. 57.
Size-dependent optical properties of ZnO NCs
Figure 1(a) shows normalized absorbance and PL spectra for three representative aliquots obtained at 2 min, 480 min, and 2400 min growth times. Those times correspond to initial, intermediate, and final NC growth stages, respectively. Figure 1(b) shows the particle diameter as a function of growth time, as measured by TEM (see Fig. S1 for images and particle population analyses). The exciton absorbance peak at 330 nm for the 2 min sample shifts to longer wavelengths with increasing reaction time. The red shift indicates that the ZnO NC bandgap energy decreases as the NC size increases,61 in agreement with TEM data in Fig. 1(b). The 480 min and 2400 min ZnO NC absorbance spectra exhibit a broad tail for λ > 400 nm. This spectral feature is due to NC aggregation and can be minimized if the NC concentration is <100 nM (Fig. S2).
The normalized PL spectra in Fig. 1(a) exhibit size-dependent features. The PL peak at λ = 360 nm for the 2 min sample can be assigned to near-band-edge recombination. The position of this PL peak shows the minimal red shift as the NCs grow, likely due to the near-band-edge state energy remaining the same as the NCs increase in size. The second PL feature is an intense and broad PL peak at λ = 550 nm in the 2 min sample, which shifts to longer wavelength with increasing reaction time. This broad PL peak has been assigned to defect emission or radiative transitions between electrons in the conduction band and holes trapped at defect states in the NC bandgap.62 The defect states have been attributed to crystallographic defects such as O vacancies (VO)62–65 and Zn vacancies (VZn)66–69 or metal dopant atoms such as Cu70,71 and Mg.72 Since ICP-AES analysis did not reveal Cu or Mg in these ZnO NCs, we attribute the defect PL peak to intrinsic defects, most likely VO, in agreement with ZnO NC samples prepared under similar reaction conditions.44,62,73 van Dijken et al. also attributed the PL peak to VO and observed a similar red shift in the defect PL peak with increasing NC size.62 Those authors attributed the red shift to a continuous decrease in band edge energy levels relative to a fixed defect energy level. In this scenario, the defect PL peak red-shifts because the energy difference between the band edges and the defect level decreases with increasing particle size. The fixed defect energy level suggests that the nature of the defect responsible for the sub-bandgap emission does not change with particle size.
Another size-dependent PL spectral feature is the decrease in the defect emission intensity with increasing NC size. Figure 1(b) shows that the defect PL QY decreases by a factor of 4 as the particle diameter and volume increase by 3- and 4-times, respectively. The decrease in defect PL QY and increase in bandgap PL suggest that the number of emissive defect states decreases. Note, the radiative recombination rate k0 is independent of NC size (Table S1). Hence, based on these size-dependent PL features, we assume that the number and locations of defects within the NCs change with reaction time, but the nature of the defect sites responsible for emission does not change with reaction time.
Energy transfer measurements
Having characterized the emission profiles and defect PL QYs of these ZnO NCs, we studied the size- and concentration-dependent EnT behavior of the NC donors in the presence of A555 acceptors. To establish that EnT occurs between defect levels in the ZnO NCs and A555, we first determined the spectral overlap of the donor–acceptor pair. Figure 2(a) shows the normalized emission of an ethanolic solution of 4.0 nm-diameter ZnO NCs compared to the absorption and emission spectra of A555. The defect emission peak overlaps with the A555 absorbance feature, which suggests that EnT will proceed via ZnO defect states rather than the band edge states. The spectral overlap persisted for all ZnO NC sizes. We calculated J and R0 for all NC donor–acceptor pairs using Eq. (5) and assuming (Table S1), following the literature.44 The assumption of randomly oriented dipoles may not be valid, as will be discussed below. The R0 values decrease with increasing particle size because both J and QD decrease with increasing particle size. Interestingly, R0 is larger than the particle radius for NCs with diameters <5.3 nm, which has important consequences for interpretation of the donor–acceptor distances determined from TRPL data.
Steady state PL measurements indicate that photo-excited ZnO NCs induce A555 fluorescence via a defect-mediated EnT process. Figure 2(b) shows the representative steady state PL spectra of 70 nM 4.0 nm-diameter ZnO NCs as a function of increasing A555 concentration. Upon exciting the bandgap of the ZnO NCs with 330 nm light, the defect emission intensity decreases over the wavelength range of 400 nm–560 nm and the A555 fluorescence peak intensity at 585 nm increases with increasing bulk concentration of A555. The A555 fluorescence peak maximum did not shift with increasing bulk concentration, suggesting that dye aggregation does not occur under these conditions. Control experiments of A555 alone excited at the same wavelength and at the same concentrations used for the mixture experiments show weak fluorescence intensity [low intensity, red dashed lines in Fig. 2(b)]. Additional control experiments show that sodium acetate does not quench the defect PL of these ZnO NCs (Fig. S4), indicated that the carboxylic acid binding moiety alone does not induce the PL quenching behavior in the presence of A555. We observed no change in the bandgap PL intensity in the presence of the acceptor, indicating that EnT stems from defect energy levels rather than the bandgap energy levels. These results agree with those of Beane et al. who studied EnT between 3.2 nm-diameter ZnO NCs and Alexa Fluor 594 dye.44
TRPL measurements show that the ZnO NC defect PL decays faster in the presence of A555 acceptors. Figure 3(a) shows representative TRPL data of 4.0 nm ZnO NCs as a function of A555 acceptor concentration. Figure S5 shows the TRPL data for all NC diameters and A555 concentrations. We measured TRPL decay data over the spectral region indicated by the dark shaded rectangles in Fig. 2 to ensure that A555 emission does not contribute to the TRPL decay measurement. The black data points represent the TRPL data of ZnO NCs alone in ethanol. In the absence of A555, the ZnO defect PL decay exhibited non-single-exponential decay kinetics, in agreement with the literature.44,73 For all NC sizes and donor–acceptor ratios, the A555 acceptor accelerates the PL decay of the NC donors.
Stochastic binding model analysis
We determined R for these ZnO NC–A555 donor–acceptor pairs by analyzing the TRPL data using the stochastic binding model.32 R represents the ensemble average donor–acceptor distance or the average distance between defects in the ZnO NCs and the molecular acceptors. To do so, we first fit the TRPL decay curve of the donor in the absence of the acceptor with Eq. (1). The black data points and red solid lines in Fig. 3(a) show representative fit results for 4.0 nm NCs in ethanol, yielding k0 = 1.4 × 10−3 ns−1 ± 1.4 × 10−5 ns−1, kqt = 0.017 ns−1 ± 9.6 × 10−5 ns−1, and λt = 2.5 ± 0.0085, in agreement with those of Beane et al. for similar size ZnO NCs.44 The photophysical parameters are independent of NC size (Table S1), suggesting that the PL QY decreases with NC size because the number of emissive defect states decreases with increasing reaction time.
Having analyzed the TRPL decay data of the NC donors alone, we attempted to fit the PL decay curves of the donors in the presence of A555 using Eq. (2). We fit λs and kq using experimentally determined values for k0, kqt, and λt that were obtained from TRPL experiments of the donor alone [i.e., Eq. (1)]. However, the error in λs and kq was large. To minimize the error in λs and kq, we performed experiments at large [A555]:[NC] ratios (e.g., >100:1 in Fig. S6) where the TRPL decay curves were independent of bulk [A555], likely because λs saturates and kq is fixed. Hence, for all NCs studied herein, we determined the energy transfer rate at a saturated bulk acceptor concentration (denoted as kq,sat). To do so, we fit TRPL decay curves at [A555]:[NC] = 1000:1 using Eq. (2), yielding λs and kq,sat values with the 95% confidence intervals shown Figs. 3(b) and 3(c). Figure 3(b) shows that kq,sat decreases with increasing NC diameter. The kq,sat trend could be due to a change in R because Förster theory predicts that kq scales with τD−1 (R0/R)6 for a single donor–acceptor pair.2 To test this hypothesis, we determined R using the SB model, which takes into account the NC size-dependent τD and R0 and importantly, that multiple acceptors may quench the PL of a single NC donor.
To quantify R, we fit the TRPL data in the low acceptor concentration regime using Eq. (3) and only one adjustable parameter, λs. The blue data points and red solid lines in Fig. 3(a) (inset) show PL decay data and fit results from 4.0 nm NCs as a function of bulk [A555]. Figure 3(c) expectedly shows that λs increases with bulk [A555] for all NC sizes studied herein. Note the small 95% confidence intervals in Fig. 3(c) that result from the aforementioned fitting procedure. We fit these data with a Langmuir adsorption isotherm [Eq. (S1), red lines] to obtain the equilibrium binding constant, K. Figure S7 shows that K is independent of NC size, indicating that the binding affinity of A555 to NC surfaces does not change with size. This result also suggests that changes in energy transfer efficiency among the different NC sizes are not due to changes in NC surface chemistry or the nature of the NC–A555 interaction.
Having determined kq and λs, we calculated ΦEnT as a function of bulk [A555] using Eq. (3). Figure 3(d) shows that ΦEnT expectedly increases with [A555] because acceptor molecules are more likely to be located within a distance R0 from the NC surface. Finally, we determined R from these ΦEnT vs bulk [A555] data using Eq. (4). We discuss how and why R changes with NC size in the section titled Discussion that follows the restricted geometry analysis.
Restricted geometry model analysis
We analyzed the TRPL datasets in Fig. 3(a) and Fig. S8 using the restricted geometry model to obtain r1, which represents the average distance between defects and the nearest A555 acceptor. Figure 4 shows Φret decay curves for 4.0 nm ZnO NCs at three representative bulk A555 concentrations. Φret represents the donor decay curve in the presence of A555 divided by the donor decay curve in the absence of A555. Fitting the TRPL data using Eq. (6) yields Cs and, importantly, r1. We converted Cs into units of dye molecules per NC and compared those values to λs in Fig. S9. There is good agreement between λs and Cs, even though the restricted geometry model does not assume that the distribution of dyes around the NCs follows Poisson statistics.
Figure 5 compares R and r1 vs NC diameter at λs 1 molecule per NC. Both values decrease with increasing NC diameter, indicating that the distance between the emissive defect sites and surface-adsorbed A555 molecules decreases as the NC size increases. Since the molecules cannot penetrate into the NC core, this trend suggests that the defects move closer to the NC/liquid interface as the NC grows. R is significantly larger than r1 and closely follows the size-dependent R0 values. In the section titled Discussion, we compare the donor–acceptor distances obtained from each model and consider whether the optical measurements and associated analyses can reveal the spatial distribution of emissive defect sites in the ZnO NCs.
Comparison of donor–acceptor distances
Can ensemble-level energy transfer measurements reveal the locations of emissive defects in semiconductor NCs? Here, we compare the D–A distances obtained from each model to the geometry of the NC–dye system and discuss the capability of each model to reveal the location of defect sites in the NCs.
Scheme 2 compares the average D–A distance obtained from the SB model (R) for small and large ZnO NCs when the defect site responsible for EnT is located either at the surface or the center of the NC. The scheme considers extreme NC–dye configurations that correspond to the minimum and maximum possible D–A values in the system. We illustrate R and R0 in Scheme 2 as circles with center positions located at the defect site and with NC size-dependent R and R0 radii as shown in Fig. 5. For the small 2.8 nm NCs, R or R0 are much larger than the particle radius [Schemes 2(a) and 2(b)]. In this situation, the SB model considers that all defect–dye configurations contribute to EnT, regardless of the position of the defect site because all surface-adsorbed dye molecules are located within R0 (ΦEnT > 0.5, indicated by purple highlight ovals in Scheme 2). Hence, the SB model cannot reveal the locations of emissive defect sites in the small ZnO NCs or, in general, when R0 is larger than the NC radius.
On the other hand, R and R0 are smaller than the NC radius for the large 6.0 nm ZnO NCs [Schemes 2(c) and 2(d)]. If the defect site is located at the NC surface as in Scheme 2(c), then dye molecules located on the opposite side of the NC exhibit ΦEnT ≪ 0.5 [indicated by white oval in Scheme 2(c)] because R for that particular NC–dye configuration is much larger than R0. If the defect site is located at the center of the NC as in Scheme 2(d), then the R values for any dye are slightly greater than R0, yielding ΦEnT < 0.5. Since ΦEnT > 0.5 for the large NCs when λs = 1 [Fig. 3(d)], the defect sites are likely not located in the center of the NCs. Hence, ensemble-level measurement and the SB model analysis can rule out the extreme case that the emissive defect sites are located at the center of large NCs. However, the SB model does not reveal further real space information regarding the location of the defects because R0 is comparable to the NC radius, and there are a wide range of possible defect–dye configurations that could contribute to EnT.
The situation changes for the RG model (Scheme 3). For the small ZnO NCs, the average D–A distance obtained from the RG model (r1) is approximately equal to the NC radius, even though R0 is still much larger than the NC [Schemes 3(a) and 3(b)]. Hence, the RG model identified a physically meaningful D–A distance that matches the geometry of the system, even though the model assumes nothing about the shape and size of the NC. While the RG model does not reveal where the defect sites are located in the small NCs for the same reasons as discussed above, the RG model apparently provides more physically meaningful results than the SB model for situations where R0 is much larger than the NC radius.
For the large NCs, the RG model predicts that the nearest possible acceptor molecule is located, on average, 0.5 nm from the defect (Fig. 5). The small separation distance strongly suggests that emissive defect sites responsible for EnT are located at the NC surface [Scheme 3(c)] instead of the core [Scheme 3(d)]. If the defects were located at the core, then we would not expect to observe EnT in TRPL measurements because core defects would be too far away from the acceptor molecules. While both models indicate that the emissive defects in the large ZnO NCs are likely located at the surface, the RG model pinpoints the location of defects to surface or near-surface locations. Hence, we conclude that the RG model has the potential to yield meaningful information regarding the real space distribution of emissive defects sites in semiconductor NCs, especially when R0 is less than the NC radius.
Size-independent EnT efficiency
We expected ΦEnT to increase with decreasing NC size because there is a higher probability that an acceptor molecule is located within a distance R0 from the defect site for the small NCs [Schemes 2(a) and 2(b) vs 2(c) and 2(d)]. However, ΦEnT ≈ 0.5 at λs = 1 for all NC sizes (see Fig. S10). One explanation for the size-independent ΦEnT behavior is that the assumption of random orientation between donors and acceptors is not valid in these systems [i.e., in Eq. (5)]. One possibility is that the small NCs have a higher concentration of defect dipoles that cannot participate in defect-mediated EnT. The small NCs likely have a higher concentration of emissive defects, but those defects may be distributed throughout the crystallites such that the orientation of the defect dipoles does not align with surface adsorbed molecules. The variable arrangement of defects in the small NCs could stem from poor crystallinity at early growth stages. It is possible that the orientation factor for the small NCs is , and therefore, the R0 values in Scheme 2 may be overestimated.
Limitations of ensemble-level defect-mediated EnT studies
Unfortunately, the ensemble-level measurement approach prevents us from directly observing the spatial distribution of emissive defects and assessing the validity of underlying assumptions of the SB and RG models (e.g., ). In addition, ensemble-level EnT measurements cannot distinguish surface-adsorbed molecules that participate in EnT from those that do not [e.g., purple shaded vs white ovals in Scheme 3(a)]. Distinguishing EnT-active vs spectator molecules could help to understand whether all molecules contribute equally to defect PL quenching, which is an assumption in the SB model. Second, both models assume that donor dipoles are located at the NC center, which is likely not valid. Single molecule, super-resolution fluorescence microscopy experiments performed at the single NC-level could overcome both limitations. Single molecule EnT experiments could pinpoint the locations of emissive defect sites and, at the same time, distinguish EnT-active from spectator molecules by selectively exciting the donor and acceptor species in the NC–dye conjugate, as Banin and co-workers showed in single molecule experiments of CdSe/CdS nanorod donors in the presence of multiple Atto 590 acceptors.74 Selective excitation of surface-bound vs bulk acceptor molecules is not possible in conventional ensemble-level experiments. Polarization-dependent single molecule EnT measurements could also reveal the orientation of the donor and acceptor dipoles, especially for nanoparticle donors with asymmetric shapes.
We studied defect-mediated EnT between ZnO NC donors and Alexa Fluor 555 acceptor molecules using TRPL measurements. We analyzed the TRPL decay curves using two different models and concluded that the RG model yielded physically meaningful donor–acceptor distance measurements that agreed with the geometry of the NC–dye system. Furthermore, the RG model predicted that emissive defect sites are, on average, 0.5 nm away from the donor molecules bound to 5 nm-diameter ZnO NCs. This study shows that ensemble-level EnT measurements have the potential to provide insight into the distribution of defects in semiconductor NCs. Understanding how the defect site distributions influence energy and charge flow between NCs and molecules could lead to the design of efficient light-harvesting NCs for photocatalysis and sensing applications.
The supplementary material includes additional synthesis and materials characterization information, tabulated kinetic parameters, TRPL fitting procedures and results, and additional control experiments.
Z.N.N. performed all experiments. Z.N.N. and J.B.S. analyzed the data and wrote this manuscript. L.M.B. contributed to experiments.
We acknowledge Dr. Duncan Ryan for assistance with IRF deconvolution, proofreading the manuscript, and providing thoughtful insight that helped us to interpret the results of this study. We thank Dr. Roy Geiss at Colorado State University for assistance with TEM imaging. Z.N.N. acknowledges Colorado State University for a PRSE summer graduate fellowship. This material is based on the work supported by the Air Force Office of Scientific Research (AFOSR) under Award No. FA9550-17-1-0255.
The data that support the findings of this study are available within the article and its supplementary material.